Heretofore, as to hair dye compositions, oxidation type hair dyes in which hair dyeing is carried out utilizing an oxidation-reduction reaction, and acidic hair dyes in which hair dyeing is carried out in the acidic condition, are known. Among these, the acidic hair dyes belong to semipermanent hair dyes, and the semipermanent hair dye is a hair dye composition in which hair is dyed by permeating the acidic dye into hair directly.
However, in the previous acidic hair dyes, aromatic alcohols such as benzyl alcohol are exclusively used as a penetration accelerator of the dye (JP, A, 5-105,615, JP, A, 8-225,435 and JP, A, 2002-104,942), and though aromatic alcohols have an action of accelerating penetration of dye into hair, they have a low water solubility, and have the problems on use such as odor at the time of hair dyeing, dripping down when applying to hair to foul cloth, and the problem of safety by irritation to skin, so that no sufficiently satisfactory hair dye has been obtained.